The saturn ring effect in nematic liquid crystals with external field: effective energy and hysteresis

Abstract

In this work we consider the Landau-de Gennes model for liquid crystals with an external electromagnetic field to model the occurrence of the saturn ring effect under the assumption of rotational equivariance. After a rescaling of the energy, a variational limit is derived. Our analysis relies on precise estimates around the singularities and the study of a radial auxiliary problem in regions, where a continuous director field exists. Studying the limit problem, we explain the transition between the dipole and saturn ring configuration and the occurrence of a hysteresis phenomenon, giving a rigorous explanation of what was conjectured previously by [H. Stark, Eur. Phys. J. B 10, 311-321 (1999)].

42 pages, 6 figures

References in corpus (4)

• Introduction to Q-tensor theory
• Orientation of topological defects in 2D nematic liquid crystals
• Saturn ring defect around a spherical particle immersed in nematic liquid crystal
• Lifting of ${\mathbb{RP}}^{d-1}$-valued maps in $BV$ and applications to uniaxial $Q$-tensors. With an appendix on an intrinsic $BV$-energy for manifold-valued maps

Cited by in corpus (5)

• Saturn ring defect around a spherical particle immersed in nematic liquid crystal
• Far-Field Expansions for Harmonic Maps and the Electrostatics Analogy in Nematic Suspensions
• Spherical Particle in Nematic Liquid Crystal with a Magnetic Field and Planar Anchoring
• Pattern Formation in Landau-de Gennes Theory
• Torus-like solutions for the Landau-de Gennes model. Part III: torus vs split minimizers